Implementation of statistical dynamic diffraction theory for defective semiconductor heterostructure modelling

Shreeman, P. K.; Matyi, R. J.

doi:10.1107/s0021889810009143

Cited by 10 publications

(17 citation statements)

References 30 publications

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“…Since it is much higher in intensity than the layer, the deviation of its shape from DDT predictions affects the curve significantly. The deviations can be due to instrumental effects or due to the influence of defects [see, for example, the paper by Shreeman & Matyi (2010), where the fit of the region near the substrate for a similar structure was obtained in the frame of statistical dynamical diffraction theory].…”

Section: Numerical Examples and Fitting Of Experimental Rocking Curvementioning

confidence: 99%

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices

Lobach¹,

Benediktovitch²,

Ulyanenkov³

2017

J Appl Cryst

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1 This article will form part of a virtual special issue of the journal, presenting some highlights of the 13th Biennial Conference on HighResolution X-ray Diffraction and Imaging (XTOP2016).Keywords: interfacial roughness; transition layers; multilayers; dynamical diffraction; recursion matrix formalism.Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices 1 Ihar Lobach, a * Andrei Benediktovitch a and Alexander Ulyanenkov b a Atomicus OOO, Minsk, Belarus, and b Atomicus GmbH, Karsruhe, Germany. *Correspondence e-mail: igor.lobach@atomicus.by Diffraction in multilayers in the presence of interfacial roughness is studied theoretically, the roughness being considered as a transition layer. Exact (within the framework of the two-beam dynamical diffraction theory) differential equations for field amplitudes in a crystalline structure with varying properties along its surface normal are obtained. An iterative scheme for approximate solution of the equations is developed. The presented approach to interfacial roughness is incorporated into the recursion matrix formalism in a way that obviates possible numerical problems. Fitting of the experimental rocking curve is performed in order to test the possibility of reconstructing the roughness value from a diffraction scan. The developed algorithm works substantially faster than the traditional approach to dealing with a transition layer (dividing it into a finite number of thin lamellae). Calculations by the proposed approach are only two to three times longer than calculations for corresponding structures with ideally sharp interfaces.

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Section: Numerical Examples and Fitting Of Experimental Rocking Curvementioning

confidence: 99%

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices

Lobach¹,

Benediktovitch²,

Ulyanenkov³

2017

J Appl Cryst

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“…The use of this approach for the analysis of highly defective layers is not recommended, however. For example, fully relaxed silicon-germanium epitaxial layers grown with high Ge concentrations on silicon substrates are very poorly described using the dynamical diffraction theory (Shreeman & Matyi, 2010), as is structurally defective ion-implanted SiGe with a range of germanium concentrations (Shreeman & Matyi, 2011). A purely dynamical analysis strategy is not appropriate for the analysis of these cases of fully or partially relaxed samples.…”

Section: Introductionmentioning

confidence: 99%

“…Fortunately, a mosaic block model based on the method of Bushuev (1989b) has been found to provide a useful simplified approach for incorporating this parameter. As discussed by Shreeman & Matyi (2010) we can use the Bushuev mosaic block model and consider only the real part of by using…”

Section: Introductionmentioning

confidence: 99%

“…We have found, however, that broadening effects due to the presence of defects in the substrate will have an impact on the diffracted amplitude and need to be incorporated into the SDDT model. This essential modification of the SDDT is detailed in recent work (Shreeman & Matyi, 2010, 2011Shreeman, 2012). In this approach the basic definition E c h ¼ R mÀ1 E c o is used, where the reflection coefficient from a given layer is defined in terms of the amplitude emerging from the material beneath.…”

Section: Introductionmentioning

confidence: 99%

“…The preceding discussion has considered only the coherent (dynamic) component of the diffracted intensity. As discussed elsewhere (Shreeman & Matyi, 2010), the incoherent or kinematic component is described by the energy transfer equations…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modified statistical dynamical diffraction theory: analysis of model SiGe heterostructures

et al. 2013

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A modified version of the statistical dynamical diffraction theory (mSDDT) permits full-pattern fitting of high-resolution X-ray diffraction scans from thinfilm systems across the entire range from fully dynamic to fully kinematic scattering. The mSDDT analysis has been applied to a set of model SiGe/Si thinfilm samples in order to define the capabilities of this approach. For defect-free materials that diffract at the dynamic limit, mSDDT analyses return structural information that is consistent with commercial dynamical diffraction simulation software. As defect levels increase and the diffraction characteristics shift towards the kinematic limit, the mSDDT provides new insights into the structural characteristics of these materials.

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Application of statistical dynamical diffraction theory to highly defective ion implanted SiGe heterostructures

Shreeman

Matyi

2011

Physica Status Solidi (a)

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The statistical dynamical diffraction theory (SDDT) provides a method for performing high resolution X-ray diffraction (HRXRD) analyses from materials that contain high levels of structural imperfection. SDDT is implemented by combining kinematical and dynamical diffraction formalisms into a single framework through the inclusion of two parameters (a static Debye-Waller factor and a correlation length) that can provide an adjustable coupling between the kinematic and dynamic extremes. Typically one of the prominent difficulties in implementing SDDT is the mathematical complexities that are characteristic of this theory. Recently we have demonstrated a simplified realization of SDDT [Shreeman and Matyi, J. Appl. Crystallogr. 43, 550 (2010)] that preserves the essential features of the theory while allowing it to be applied to a variety of structures. Here we show the viability of this approach by fitting various experimental HRXRD data from highly defective and partially relaxed Si 0.70 Ge 0.30 ion implanted heterostructures. This study demonstrates the capabilities the SDDT theory provides for HRXRD analyses of highly defective semiconductor materials.

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Implementation of statistical dynamic diffraction theory for defective semiconductor heterostructure modelling

Cited by 10 publications

References 30 publications

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices

Modified statistical dynamical diffraction theory: analysis of model SiGe heterostructures

Application of statistical dynamical diffraction theory to highly defective ion implanted SiGe heterostructures

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